Overall Objectives
Research Program
Application Domains
New Software and Platforms
New Results
Partnerships and Cooperations
XML PDF e-pub
PDF e-Pub

Section: New Results

A Type-Based Analysis of Causality Loops In Hybrid Systems Modelers

Explicit hybrid systems modelers like Simulink / Stateflow allow for programming both discrete- and continuous-time behaviors with complex interactions between them. A key issue in their compilation is the static detection of algebraic or causality loops. Such loops can cause simulations to deadlock and prevent the generation of statically scheduled code. In [6] (also published as a deliverable of the Sys2Soft collaborative project  [14] , see  8.2 ), we address this issue for a hybrid modeling language that combines synchronous Lustre-like data-flow equations with Ordinary Differential Equations (ODEs). We introduce the operator last(x) for the left-limit of a signal x. This operator is used to break causality loops and permits a uniform treatment of discrete and continuous state variables. The semantics relies on non-standard analysis, defining an execution as a sequence of infinitesimally small steps. A signal is deemed causally correct when it can be computed sequentially and only progresses by infinitesimal steps outside of discrete events. The causality analysis takes the form of a simple type system. In well-typed programs, signals are proved continuous during integration and can be translated into sequential code for integration with off-the-shelf ODE solvers. The effectiveness of this system is illustrated with several examples written in Zélus, a Lustre-like synchronous language extended with hierarchical automata and ODEs.